Shading is important for estimation of three-dimensional shape from the two-dimensional image, for instance, for distinguishing between the smooth occluding contour generated by the edge of a sphere and the sharp occluding contour generated by the edge of a disk. In order to use shading information to solve such problems, one must know the illuminant direction L. This is because variations in image intensity (shading) are caused by changes in surface orientation relative to the illuminant. Each illuminant direction L has a unique effect on the distribution of changes in image intensity dI, potentially permitting the estimation of L. However, because dI is a function of bothL and the surface curvature, L can be estimated from the image only by making an assumption about the imaged surface curvature. One assumption that is sufficient to disentangle L and surface curvature is that changes in surface orientation are isotropically distributed. This condition is true of images of convex objects bounded by a smooth occluding contour and is true on average over all scenes. Estimates made by using this assumption agree with estimates of illuminant direction given by human subjects for images of natural objects, even when both are objectively wrong. Further, there is a significant correlation between the variance of these estimates and the variance of the human subjects’ estimates.
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